Members of a group of Honduran migrants, which included a mother who had been photographed running with her daughters from tear gas several weeks ago, began seeking asylum at the U.S. border with Mexico on Monday, according to a Reuters witness and lawyers for the group.

A young Guatemalan girl who died after she and her father were detained by U.S. border agents was in no medical distress when they arrived and had received adequate food and water on their journey, relatives said on Saturday through representatives in Texas.

Thousands of Central American migrants are digging in for a long haul at a filthy, overcrowded sports complex in sight of the United States, while a small number have opted to return home after clashes with border forces dimmed hopes of crossing.